By Philip James
Alex Bogdanovic 6-2 6-4 Adam El Mihdawy
Bogdanovic, 28, is playing in only his second Challenger tournament of the year, the first of which was in Dallas where he navigated qualifying but lost in round one.
Though ranked 45 places below Bogdanovic, El Mihdawy had already won two qualifying matches before eliminating the number two seed, Malek Jaziri, in the first round.
However the British number five was two strong for the American and won 6-2 6-4 in just over an hour.
Bogdanovic, ranked 310 in the world, played solid tennis, barely losing a point on his first serve and saved the only two break points his opponent created.
He will play another qualifier, 343-ranked Rik De Voest of South Africa, in the quarter-final last thing on Court Central this evening.
Baker, ranked 209, was unlucky enough to be drawn against defending champion and top seeded Canadian Vasek Pospisil.
He battled well against a player ranked 80 places above him, eventually losing to in a third set tie-break 6-4 3-6 7-6(5).